Find the volume of the solid of revolution obtained by revolving the plane regio

Calculus
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Find the volume of the solid of revolution obtained by revolving the plane region bounded by , the -axis, and the line about the -axis.

Apr 26th, 2015

If the region is bounded by the x-axis and the graph y = f(x) and the solid is obtained by rotating the region about the x-axis, then we need to find the integral π∫ab f2(x) dx, where either the interval a ≤ x ≤ b is given or its endpoints are found as x-intercepts of the graph y = f(x).

In case when the region is bounded by the vertical lines x = a, x = b, and the graphs y = f1(x) and y=f2(x), where f1(x) ≤ f2(x) for a ≤ x ≤ b, the volume of the solid obtained by revolution of the region about the x-axis equals π∫ab [f22(x) ‒ f12(x)]dx.

PS. If you have specific questions about this volume, please let me know.


Apr 25th, 2015

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